WASHINGTON (CNN) - The Senate should wrap up work on a sweeping overhaul of U.S. immigration laws before the Fourth of July, but its odds of passage remain uncertain, the chamber's Republican leader said Sunday.

Despite an agreement last week that revived the White House-backed measure, "It's hard to know whether the votes will be there to pass it or not," Minority Leader Mitch McConnell told CBS' "Face the Nation."

McConnell predicted the Senate would wrap up work on the measure "one way or the other" before the holiday.

Senate Majority Leader Harry Reid, D-Nev., yanked the bill off the floor June 7 after supporters failed to muster the votes necessary to cut off debate on a series of amendments that were nibbling away at the delicate political balance the bill's authors had crafted. But Senate leaders agreed to bring the measure back after reaching a deal to consider about 20 amendments, split evenly between Democratic and Republican proposals.

The measure would create a guest-worker program to let migrant workers from other countries work temporarily in the United States, a plan that critics have said would create a permanent underclass of poor, low-skill workers.

But the bill's most controversial aspect is the creation of a pathway to legal status and eventual citizenship for the estimated 12 million illegal immigrants already in the country - a plan critics denounce as "amnesty."

Bush has made reforming U.S. immigration law a top priority for his second term, and Thursday's breakthrough came after he backed an amendment that would that would use $4.4 billion in fees raised by the legislation to boost border security and prevent illegal immigrants from being hired in workplaces.

The bill drew support from just seven Republicans on the procedural motion that led to it being shelved, along with 37 Democrats and one independent - a total of 15 votes shy of the 60 needed to move forward. Reid said Bush needed to bring more GOP allies around to supporting the bill, and Bush's proposal was an effort to woo critics who say the bill needs to place more emphasis on border security.

But the plan still has its critics in both houses of Congress, and Rep. Duncan Hunter, R-Calif., told CNN's "Late Edition with Wolf Blitzer" that the Bush-backed amendment is "a terrible trade."

"Border security is the obligation of the American government," said Hunter, a GOP presidential candidate. "That's like saying we'll send enough bullets to our troops in the field in Iraq or Afghanistan if you do something else, if you in Congress will make the right move. That should be a given."

Sen. John Cornyn, R-Texas, called Bush's plan "a good idea." But he added, "That alone is not going to satisfy the concerns about whether we are really going to build a workable system."

"Part of the problem is the American people look at this and they remember what happened in '86, when they were told, if you'll accept a one-time amnesty, then we'll get true enforcement," he told CNN. "Well, we all know what happened. We got an amnesty, but no enforcement."

But Sen. Lindsey Graham, R-S.C., said it would be "political malpractice" to simply focus on current law without addressing the status of the immigrants now in the United States illegally.

"This is no longer about immigration reform. This is about, can we govern ourselves?" Graham said. "Can Republicans and Democrats sit down at a table and do the hard things, or are those days behind us? I am confident that the Senate will deliver."

soundoff(2 Responses)

This IS about immigration reform. When the federal government does not excerise its Constitutional duties to protect our Country from enemies foreign and domestic than this Country has a huge problem. This is not a Democratic or Republican issue.

I am an Independent. Most of my friends and relatives are minority Democrats and they HATE, HATE, the immigration bill Congress is trying to shove down our throats.

I don't believe the polls that indicate that the majority of Americans are for this immigration bill. None of my friends, nor myself have ever been called or asked our opinion in any of these national polls. I'd like to know who those 300- 1000 people are that the media cites to say AMERICANS agree with the immigration bill.

The Republicans are always going around saying they can protect the Country from terrorists, yet, they have allowed our borders to remain WIDE open for almost 8 years and almost 7 years since 9/11.

Please someone put Americans first for once.

The entire Congress is shameful because they do not want to enforce the rule of law for the illegals, yet, if you are an American citizen, we'd better obey every law or else we'd get thrown into the legal system. What the hell kind of lesson is that!

This is 1986 all over again. But, this time instead of 3 million and all of their relatives, we will now have 12-20 million and all of their relatives. How is the Country going to absorb all of those folks into our social welfare, education, and medical systems?? I can see my tax dollars now going to support illegals and I can almost smell a tax increase coming my way. I sick of the middle class being expected to support the Country and the folly of Congress.

The United States Senate has become a pawn of special interests, and special interests only – your Senator, my Senator, all of them. Face it, that this bill could even be considered means representative democracy is dead in America, as is a media that fairly represents the people.

Folks this is your last chance – write, or better yet call or visit your representatives, your party headquarters, your local representatives and tell them that this bill MUST be rejected.

Otherwise don't complain about afterwards, whe your children or grandchildren are crowded out of a job.